If you know about how to get 50K real likes which from human instead of the auto bot, you should know about to increase from the 50K likes to 1 million likes. Because getting 50K real likes is not easy.

Speed of getting new likes influenced by trend factor. If you create a FB page which related to hot topic and almost no competition then the FB page can get loads of new likes quickly. And make sure to keep update it to speed spreading process.

I'm not a big social media user, but I have tried and tested FB. One thing I found was that getting Likes takes off exponentially when you find something current that people are passionate about. For example, if you're in the food industry you have to watch all the food shows, know what's going on and when something pops onto the scene that is new and exciting, you need to be one of the first to take on the subject. The more controversial, the better, but keep it on-topic. You don't want to do politics on a food page.

Facebook advertising is best way to achieve more likes faster. But high amount of likes(1 million likes) in short period cannot be looks like as a real likes. Frequent sharing in groups with useful post will helps you to get more likes. Try to share video or image it works better than other.